Problem: Simplify the following expression: $ a = -6 + \dfrac{3}{-7k + 10} $
Solution: In order to add expressions, they must have a common denominator. Multiply the first expression by $\dfrac{-7k + 10}{-7k + 10}$ $ \dfrac{-6}{1} \times \dfrac{-7k + 10}{-7k + 10} = \dfrac{42k - 60}{-7k + 10} $ Therefore $ a = \dfrac{42k - 60}{-7k + 10} + \dfrac{3}{-7k + 10} $ Now the expressions have the same denominator we can simply add the numerators: $a = \dfrac{42k - 60 + 3}{-7k + 10} $ $a = \dfrac{42k - 57}{-7k + 10}$ Simplify the expression by dividing the numerator and denominator by -1: $a = \dfrac{-42k + 57}{7k - 10}$